GENERALIZED Ψ-GERAGHTY-QUASI CONTRACTIONS IN b-METRIC SPACES

In this paper we generalize the well-known class of quasi contractions pairs, by using the so-called Geraghty's property and by controlling the contractive inequality with an altering distance function. For this class, in the setting of b-metric spaces, we prove the existence and uniqueness a of common fixed point assuming some non commutative notions. Finally, for this class of mappings we prove the b-convergence of the Jungck-Mann iterative scheme under suitable conditions on the b-metric space and on the altering distance function.